$$C^{1, 1}$$ regularity for solutions to the degenerate $$L_p$$ Dual Minkowski problem

Chen, Li; Tu, Qiang; Wu, Di; Ni, Xiang

doi:10.1007/s00526-021-01975-x

Cited by 3 publications

(1 citation statement)

References 41 publications

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“…For the classical degenerate Monge-Ampère equation, C 1,1 solutions are found in [41,44]. Similar results for Minkowski type problem can be found in [21,42]. For the flows with degeneracy, we refer readers to [28,29,31,36,53] for surfaces with flat sides and [55] for surfaces with an obstacle.…”

Section: Introductionsupporting

confidence: 70%

Regional classification according to PM10 concentrations in the Seoul Metropolitan and Chungcheong Area, Republic of Korea

Ho¹

2023

Preprint

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Since the Seoul Metropolitan Area, Republic of Korea, is highly populated, a large number of people are frequently exposed to high concentrations of particulate matter (PM) with mean aerodynamic diameters of <= 10 mm (PM10) in cold season. The concentration of PM10 in Seoul Metropolitan Area increases by transboundary transport, local direct emissions, and chemical reactions of aerosol precursors in the atmosphere. Here, the Seoul Metropolitan Area (Seoul, Gyeonggi-do, and Incheon) and surrounding region (Chungcheongnam-do, Daejeon, and Sejong) are regionally classified by clustering analysis based on the variability of PM10 concentrations. According to the inertia score by the number of clusters, the optimum cluster number of regional variability of PM10 is four. The region of cluster 1 is divided into southern Gyeonggi-do and eastern Chungcheongnam-do, the cluster 2 is mainly classified Incheon, western Gyeonggi-do, and Seoul. The cluster 3 region is western Chungcheongnam-do adjacent to Yellow Sea, and the cluster 4 is classified into eastern Gyeonggi-do. The variability of PM10 in each region is distinguished by the local chemical pollutants emission and weather conditions such as wind speed and direction in each region. This regional classification of PM10 variability is different from administrative districts. Considering most of policies for responding to high concentrations of PM10 are being prepared by administrative districts, this study suggests that a response on the basis of these regional PM10 distribution would be more effective way to improve air quality in the Seoul Metropolitan and Chungcheong Area.

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